2024/05/02 by Ryan C. Chen, Chen, Ryan C.
Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Representation Theory (math.RT) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2405.01427
openalex publication_date 2024/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is the second in a sequence of four papers, where we prove the arithmetic Siegel--Weil formula in co-rank 1 for Kudla--Rapoport special cycles on exotic smooth integral models of unitary Shimura varieties of arbitrarily large even arithmetic dimension. Our arithmetic Siegel--Weil formula implies that degrees of Kudla--Rapoport arithmetic special 1-cycles are encoded in the first derivatives of unitary Eisenstein series Fourier coefficients. In this paper, we formulate and prove the key Archimedean local theorem. In the case of purely Archimedean intersection numbers, we also prove an Archimedean local arithmetic Siegel--Weil formula, relating Green currents of arbitrary degree and off-central derivatives of local Whittaker functions. The crucial input is a new limiting method, which is structurally parallel to our strategy at non-Archimedean places.